The Northern Irishman said his family had found it difficult to settle in Glasgow during lockdown.
The new job will see Bell return to Cheltenham, a place his family have regarded as home in recent years.
He will stay with Glasgow and work with head coach Danny Wilson for the club’s remaining Rainbow Cup fixtures, against Dragons on May 29 and Leinster on June 4.
“It is with sadness that I have had to make this decision,” Bell told glasgowwarriors.org.
“My family have struggled to settle in a new city under the very difficult circumstances that Covid has created, and I am fortunate to have been given the opportunity to take them back to a place they have regarded as home for the past six years.
“This move also affords me the opportunity to work once again with Alan Solomons and be part of his exciting plans for Worcester Warriors.
“I am hugely grateful to Danny, Al [Kellock, managing director] and all the players and staff at Glasgow Warriors for their friendship and support during the year.”
Wilson said: “Thank you to Jonny for his excellent and hard work this season, particularly having moved his family to a new city in very difficult circumstances.
“As a club we recognise family comes first, and though it is a shame to lose Jonny we are completely supportive of this move.”